Let’s Play Math!

This page lists a wide-ranging assortment of math websites. Some of them I have used and enjoyed for years; others I just stumbled across while browsing and thought they looked interesting. Most of these resources are free, but I have also included a few sites that ask for a nominal fee — like Multiflyer — because I thought their product was well worth the cost.

Within each category, websites are listed alphabetically, to avoid playing favorites. I hope there is something here you will find useful. And if you know of a great site I have missed, please send me an email (there’s a link on the “About Denise” page). I appreciate your help!

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“Table of Contents” quicklinks

Studious stuff:

• Worksheets and math practice
• Study on your own with online math lessons
• Writing to learn math (all ages)
• Forums where you can ask for help

Fun stuff:

• Online games and activities
• Math contests — grades 4-12
• General math resources — high school and up
• Math history on the Internet

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Worksheets and math practice

Daily Math Review
Three years’ worth of math review (7 assorted problems per day) for grades 6, 7, and 8 — with answers provided for the busy teacher.

Donna Young’s Math Pages
Worksheets, charts, drill pages, fraction manipulatives, triangular flashcards, and more — plus a great introduction to unit multipliers (also known as conversion factors).

Free Math Worksheets from HomeSchoolMath.net
A variety of worksheets from the author of the Math Mammoth books (and Homeschool Math Blog), with links at the bottom of the page for more freebies.

GetSmarter.org
Try your hand at math and science test questions, and then see how your answers compare to those from students around the world.

MathCounts Drills by Elias Saab
Tough online practice problems for MathCounts preparation, or simply to see if you can handle the challenge. Problems are also available one by one.

Math Drills Homepage
Online mathematics tests and drills for many topics, elementary through university level.

Math Worksheet Generators
“Just the facts, ma’am.” Plenty of formatting choices.

Math Worksheet Site
My personal favorite online generator for basic math worksheets. They also offer a subscription service, if you need a wider choice of topics.

Multiflyer
Online or downloadable game for practicing the multiplication facts. This is the best math fact game I have seen, at a can’t-beat-it price.

Preparation Drills for the SAT-Math Sections
Quiz yourself online to prepare for high-stakes high school testing.

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Study on your own with online math lessons

Quicklinks for easy browsing:

• Arithmetic and other elementary topics
• Algebra and beyond

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Arithmetic and other elementary topics

HomeschoolMath.net
Place value, adding and subtracting, multiplying and dividing, fractions, and more.

Interactivate
Lots of projects to try, mostly at the elementary to middle-school level.

Math.com
Basic math, everyday math, and “hot subjects” like fractions and decimals.

Mathematics at Free-Ed.Net
Arithmetic and pre-algebra.

Problem Solving Strategies
Teach your students to solve problems—by solving problems!

Smartkiddies Math
A complete elementary math program developed by Australian teachers. [Edited to add: This used to be free. I just noticed that they now offer a 14-day free trial, but regular access is $30/year per family. It's a very reasonable price, but not as good a deal as it used to be!]

Suzanne’s Math Lessons
For upper-elementary and middle school.

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Algebra and beyond

College Algebra Tutorial
Just what it sounds like. Includes practice tests.

Dansmath Lessons
A quick review of the basics, then on to the good stuff.

Discovering Trigonometry
A basic introduction to trigonometry, starting with sticks and shadows.

HomeschoolMath.net
High school proofs, and scroll down for geometry lessons.

Interactivate
Scroll down for lessons on algebra, geometry, probability, statistics, and discrete mathematics.

Interactivate Mathematics
(A different site from the above.) From algebra and money math to higher calculus, this website (by the author of SquareCircleZ blog) has interactive Flash-based activities that help the user to understand what is going on.

Mathematics at Free-Ed.Net
Scroll down for algebra and beyond.

Math for Morons Like Us
Pre-algebra through calculus topics. With a name like that, it has to be a fun site, doesn’t it?

Math.com
Pre-algebra through calculus topics.

Math Open Reference (Geometry)
The name of the website implies more, but all I can find for now is Euclidean geometry. Plenty of Java to play with. This site makes a great follow-up for Purplemath algebra (below)—when your geometry textbook just doesn’t make sense, look here for help. The step-by-step constructions are particularly fun.

National Repository of Online Courses
Algebra, introductory calculus, and AP calculus.

Purplemath
My favorite site for supplemental lessons in pre-algebra and algebra. When your textbook just doesn’t make sense, look here for help.

S.O.S. Math
Algebra, trigonometry, calculus, and much more. This site will help college students, too.

SparkNotes Math
Pre-algebra through calculus.

Trig Without Tears
“Or, How to Remember Trigonometric Identities.” How to learn and understand trigonometry without memorizing a gazillion identities. Check out the author’s other mathematics articles, too.

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Writing to learn math (all ages)

Quicklinks for easy browsing:

• Math journaling in general
• How to get elementary students writing about math
• Journal topics for older students

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Math journaling in general

59 Writing Prompts for Math Teachers (pdf 58KB)
Title is self-explanatory. From misterteacher.com.

Logistics of Math Journals: Frequently Asked Questions (pdf 105KB)
Tips for using math journals in the classroom, by the authors of this math journaling lesson for grades 3-5.

Math Journals Boost Real Learning
An article by Marilyn Burns in Scholastic Instructor magazine, April 2001. Math journals “help students stretch their thinking and make sense of problems,” and they can help teachers evaluate student progress.

Options for Writing in Math (pdf 61KB)
Five categories of writing assignments, with sample entries by elementary students. Adapted (with permission, I hope) from an article by Marilyn Burns.

Other Writing Strategies
More topics and ideas for student writing, such as short stories, math autobiographies, or letters to a young student. Most of these will require more time and thought than the typical “writing prompt” question.

Using Writing in Mathematics
When and how to introduce math journaling, and how to move from feeling-oriented, open-ended questions to more specifically mathematical thinking and writing. Heavy use of the term “metacognition,” with examples from teachers’ journal writing about using math journals.

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How to get elementary students writing about math

Math Journals and Other Math Ideas for Primary Grade Teachers
Journaling tips and story problems based on children’s literature for kindergarten and early elementary students.

Math Journal Ideas
A list of 30 writing prompts from a Catholic homeschooling mom.

Writing in Mathematics
Mathwire.com’s September 2007 Back-to-School Issue: How to use writing in an elementary math class, with several links to articles and lesson ideas.

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Journal topics for older students

MathNotations blog
Challenging problems and investigations for grades 7-12, with an emphasis on developing conceptual understanding in mathematics. The sidebar holds a detailed topic list, making it easy to scroll down and find whatever your student needs to practice.

Thinking Mathematically
A book that will lead the junior-high through adult-level student step by step, using a journal to think your way through challenging math problems—including what to do when you are stuck and can’t find a solution. Many of the problems used as examples are traditional brain teasers and recreational math puzzles.

Using Art Projects to Create a Math Adventure…
See how a high school algebra teacher uses a math journaling project as the centerpiece of his curriculum. Photo-heavy page, but worth waiting for, even on a slow dial-up connection like mine. Students use fine-point permanent markers and quality colored pencils in artists’ sketchbooks, and then they sponge the pages of their journal with coffee for a beautiful, parchment-like effect.

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Forums where you can ask for help

Art of Problem Solving Forum
For middle school and older students. There are forums for classroom basics, but most of the AoPS forums focus on working through challenging problems and preparing for math contests.

Ask Dr. Math
Browse the archives of the Math Forum, or ask a new question by email.

Mrs. Glosser’s Math Forums
Help for elementary through high school students.

S.O.S. CyberBoard
A topical help forum for high school and college-level mathematics, engineering, computer science, and more.

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Online games and activities

Quicklinks for easy browsing:

• Elementary games and activities
• Middle school (or junior high) games and activities

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Elementary games and activities

[Also look at Math history for elementary/middle-school students, below.]

Brainwave
A mental arithmetic quiz for early elementary students: “What is half of 10?…”

Braintwister
A mental arithmetic quiz for middle elementary students: “There are 35 children in a class. 16 are boys. How many are girls?…”

Brain Teasers
Weekly questions, with hints, for grades 3-4 and higher.

Button Beach Challenge
“A taster of our forthcoming Oddsocks — The Land of the Lost interactive web based mental maths adventure.” This addition puzzle is harder than it looks. I can’t wait to try the rest of the adventure…

Callum’s Addition Pyramid
“Can you open the Mummy’s Tomb?” With three difficulty levels, this will challenge any elementary student’s mental addition skills — and many adults’ skills, too!

CSU Problem of the Week
More weekly puzzles, elementary level. An “honor roll” is posted of students who send in the correct answer.

Fun Mathematics Lessons by Cynthia Lanius
A wide variety of topics for a wide range of ages.

Math Cats
Math explorations, crafts, homemade manipulatives, and lots of fun.

Math Playground
A ton of games and math activities, but the site was not loading properly the last time I visited, and it came up so slowly on my old dial-up connection that I lost patience. Worth a try, when it works.

National Library of Virtual Manipulatives
A treasure-chest of virtual hands-on math. Includes links to material for all ages and topics, pre-K through 12th grade.

Nrich.maths.org
Math puzzles and activities for all ages, with a theme that changes each month. Hints available, and solutions for past problems.

Taxicab Treasure Hunt
A game based on the non-Euclidean geometry of city streets.

The Table Trees
Practice your times tables, with a twist — it’s not always the answer that’s missing.

Thinking Blocks
Learn to solve word problems by modeling them with blocks. A visual approach to thinking things through.

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Middle school (or junior high) games and activities

[Also look at Math history for elementary/middle-school students, below.]

1000 Problems to Enjoy
A large collection of challenge problems for grades 7-9, or for anyone who wants to play around with math and logic. Answers are in the Doc files, but don’t peek. Figure it out for yourself, and use the file only to check your work. It’s no fun when someone just gives you the answer!

Ambleweb Function Machine
Choose the type of problem you want to guess, or go random for more challenge. My math club kids LOVE function machines.

Brain Teasers
Weekly questions, with hints, for grades 5-6 and 7-8.

CSU Problem of the Week
More weekly puzzles, middle school level. An “honor roll” is posted of students who send in the correct answer.

Dansmath Kids Page
Puzzles, problems, and math in the real world.

Fun Math by Cynthia Lanius
A wide variety of topics for a wide range of ages.

Head Hunters Game
A bloody fun game for the Viking in all of us. If you enjoy that one, try the other math tricks and games at Murderous Maths.

Hex-a-hop
My all-time (so far) favorite logic game. “There is no time limit and no real-time elements. The objective is simply to destroy all the green hexagonal tiles on each of the 100 levels. As you progress through the game, more types of tiles are introduced which make things more difficult and interesting.” For all ages.

Hexa-Trex Puzzle of the Day
“Object of the game: Find a path through all the tiles to make a math equation.” Difficulty ranges from easy to quite challenging.

How to Count to 1,023 on Your Fingers
A Java applet teaches you to count in binary or other bases. This can extend your counting range, but “caution is advised as the number four is prone to offend onlookers.”

MathCounts Student Pages
Featuring the Problem of the Week and archives of past problems.

MegaMath
Math research projects for students from the Los Alamos National Laboratory.

Multiplication: An Adventure in Number Sense
Explore the multiplication table and discover some interesting things about how numbers work.

National Library of Virtual Manipulatives
A treasure-chest of virtual hands-on math. Includes links to material for all ages and topics, pre-K through 12th grade.

Nrich.maths.org
Math puzzles and activities for all ages, with a theme that changes each month. Plenty of interesting puzzles in the archives, too. Hints available, and solutions for past problems.

Problems? No Problem!
Quiz includes some geometry: “What is the name of an angle greater than 90 degrees but less than 180 degrees?…”

Taxicab Treasure Hunt
A game based on the non-Euclidean geometry of city streets. Follow this up with more research into taxicab geometry.

The Braindrainer
A mental arithmetic quiz for upper elementary or middle school students: “Is 4 a factor of 106?…”

The Fractotron
You will have to work fast with this game. The questions are not super-difficult, but it doesn’t give you much time to think.

The MegaPenny Project
How many does it take to pile up a ton of pennies?

The Totally Mental Machine
Random numbers make a new set of problems every time: “What is 15.7 and 4.7 together?…”

Tim’s Interactive Puzzle Solution Center
A fun collection of “famous and other curious brain teasers” to solve online, some relatively easy and some quite challenging.

Ratio Word Problems
Learn to solve ratio problems by modeling them with blocks. A visual approach to thinking things through.

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Math contests—grades 4-12

(Most of these require a registration fee, and most do not accept individuals to compete. Organize teams through your school or homeshool group.)

American Mathematics Competitions
Middle school through high school teams. Students compete individually at their own schools, then scores are compared nationally. Awards given at school and national levels. No travel required. Past tests available through the website for study and practice.

Mandlebrot Competition
High school teams. Students compete individually and in teams of four. Ribbons given to top four scorers at the school level, additional awards at the national level. No travel required.

MathCounts
Middle school teams (grades 5-8 ). Students compete individually at the school level. Each school or homeschool group may send a team of four students to a regional competition, with the top teams progressing to state and national contests (travel required). Study resources available through the MathCounts website and at these links:

• Last year’s school, chapter, and state-level tests
• MathCounts Drills by Elias Saab

Mathematical Olympiads for Elementary and Middle Schools
Elementary (grades 4-6) and middle school (grades 6-8 ) teams. Five monthly contests during the school year, no travel required. Students compete individually in their own schools or homeschool groups—with certificates for everyone and a top-scorer trophy—and then scores are compared nationally for additional awards. Low stress and lots of fun for beginning mathletes.

USA Mathematical Talent Search
High school, or advanced junior high individuals. Free. Students must solve challenging problems and write well-justified solutions. Four rounds per year, five problems per round, with one month to work each set. Past problem sets available through the website for study and practice.

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General math resources—high school and up

CSU Problems of the Week
This link takes you to the main Problem of the Week puzzle. There is also an Algebra in Action puzzle and other puzzles for younger students.

Cut the Knot Interactive
“Mathematics Miscellany and Puzzles,” many of which require Java. One of my all-time favorite sites.

Free Online Graph Paper
PDFs galore for any graphing project.

Geometry
Various notes, tidbits, equations, and diagrams—2D, 3D, and more. Scroll down for polyhedra, including a link to build your own models.

Hex-a-hop
My all-time (so far) favorite logic game. “There is no time limit and no real-time elements. The objective is simply to destroy all the green hexagonal tiles on each of the 100 levels. As you progress through the game, more types of tiles are introduced which make things more difficult and interesting.” For all ages.

How to Read Mathematics
The title is self-explanatory.

Mathematical Quotation Server
I love quotations! No matter what I want to say, somebody else has probably already said it better.

Mathematically Correct
Articles about the current U.S. “Math Wars” and reviews of many math textbooks.

Mathematics Articles by Stan Brown
Articles about how to succeed as a math student, how to use a graphing calculator, and other topics from algebra, trig, calculus, and statistics.

Number Gossip
“Everything you always wanted to know about your favorite number, but were afraid to ask.”

NYC HOLD
More articles about mathematics education and the “Math Wars.”

Proofs without words
I love these!

Recreational Mathematics
Part of Wolfram MathWorld: games, art, humor, and more.

The Math Forum
“The Math Forum is a leading center for mathematics and mathematics education on the Internet.” Enough resources and links to get lost in.

What’s Special About This Number?
Distinctive facts about several numbers: 0-9999 the last time I looked.

Wolfram MathWorld
The best online reference I know for anything related to math.

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Math history on the Internet

Quicklinks for easy browsing:

• Most valuable sites
• General resources
• Math topics & significant individuals
• Specific cultures or time periods
• Math history for elementary/middle-school students

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Math history > Most valuable sites

The MacTutor History of Mathematics Archive
My favorite place to begin any foray into math history. Highlights include:

• An Overview of the History of Mathematics
• Biographies Index
• History Topics Index
• Famous curves index
• Mathematicians of the day
• A Time Line of Mathematicians

La Habra High School’s Math History Timeline
Math discoveries, publications, and other tidbits — from paleolithic number bones to the present.

• Pre-historic and Ancient Times 1,000,000 B.C. - 500 A.D.
• Middle Ages 500 - 1400 A.D.
• Renaissance 1400 - 1550 A.D.
• Reformation 1517-1598 A.D.
• Baroque Era 1600-1700 A.D.
• Enlightenment 1700-1789 A.D.
• Age of Revolutions 1789-1848 A.D.
• Age of Liberalism 1848-1914 A.D.
• 20th Century … 1914-present A.D.

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Math history > General resources

Biographies at Wolfram MathWorld
Long, long list, and each biography is linked to explanations of the mathematician’s major discoveries.

Biographies of Women Mathematicians
Indexed alphabetically, chronologically, and by country of birth. Includes modern news tidbits, too.

A Completely Inadequate Bibliography of the History of Mathematics
“Most of the following books are aimed at the professional non-mathematician (i.e., someone to whom the land of mathematics is an interesting place to visit, but you wouldn’t want to live there).”

Convergence
An online magazine from the MAA: “Where mathematics, history, and teaching interact.”

Fred Rickey’s History of Mathematics Page
Includes Teaching a Course in the History of Mathematics and An Annotated Bibliography.

Galileo and Einstein: Overview and Lecture Index
Lecture notes on the history of math and physics.

Mathematicians of the 17th and 18th Centuries
Adapted from A Short Account of the History of Mathematics, by W. W. Rouse Ball.

Mathematicians of the African Diaspora
Black men and women of mathematics, in history and in the present.

Mathematical Quotation Server
I love quotations! No matter what I want to say, somebody else has probably already said it better.

Math Forum History Listings
“651 items found.” No, I have not checked them all. Go browse for yourself!

Math History and Mathematicians Pages
Julie Brennan at Living Math is building an index of links to biographical information, famous quotes, activities and book suggestions to accompany a homeschool math history course. [Sample lessons.] The last time I visited, she had almost finished the first year’s listings.

Philosophy of Science
Many assorted links to readings for a college class, including several chapters from String, Straightedge & Shadow.

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Math history > By topic

Abacus: The Art of Calculating with Beads
The abacus through history, how to make and use an abacus, and classroom ideas.

Archimedes
“This site is a collection of Archimedean miscellanea under continual development.” See also: Prehistoric Calculus: Discovering Pi, Archimedes’ Approximation of Pi, and The Archimedes Palimpsest.

Carl Friedrich Gauss
Detailed biography, quotations, and more.

Earliest Known Uses Of Common Mathematical Symbols and Words
Research is ongoing (I found a page that had been modified last week), so don’t assume that a citation is the earliest use unless indicated as such.

Euclid’s Elements
David E. Joyce brings the text of Euclid’s 13 Books to life with Java applets. See also: An Introduction to the Works of Euclid.

Famous Problems in the History of Mathematics
This site includes problems, paradoxes, and proofs that have inspired mathematicians through the ages, plus links for further exploration.

A Golden Sales Pitch
“There is little evidence to suggest that the golden ratio has any special aesthetic appeal… When a myth is repeated over and over, it begins to sound like truth.”

The History of Measurement
“There were unbelievably many different measurement systems developed in early times, most of them only being used in a small locality.”

Hypatia of Alexandria
Lots of links, including The Primary Sources for the Life and Work of Hypatia of Alexandria. See also: Hypatia, the First Known Woman Mathematician.

MacTutor Topical Indexes

• Algebra
• Analysis
• Geometry and Topology
• Numbers and Number Theory
• Mathematical Astronomy
• Mathematical Physics

Mathematical games and recreations
“The whole history of mathematics is interwoven with mathematical games which have led to the study of many areas of mathematics.”

The Mathematical Problems of David Hilbert
With a link to Hilbert’s 1900 address to the International Congress of Mathematicians in Paris, surely the most influential speech ever given about mathematics. Wolfram MathWorld has an annotated list of all 23 problems.

MathPages History Topics
A wide assortment of tidbits for advanced students.

Slide Rule History
“The slide rule has a long and distinguished ancestry … from William Oughtred in 1622 to the Apollo missions to the moon.”

Who was Fibonacci?
“A brief biographical sketch of Fibonacci, his life, times and mathematical achievements.”

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Math history > Cultures or time periods

Ancient Africa
Part of the Mathematicians of the African Diaspora website.

History of Egyptian and Mesopotamian Mathematics Page
An excellent resource for my Alexandria Jones stories.

History of Mathematical Education
What topics of mathematics have been taught in different cultures and time periods? Why have these changed?

MacTutor Mathematics in Various Cultures

• Ancient Babylonian mathematics
• Ancient Egyptian mathematics
• Ancient Greek mathematics
• Arabic mathematics
• Chinese mathematics
• Indian mathematics
• Mayan mathematics
• American mathematics
• Mathematics in Scotland

Mathematics in Specific Cultures, Periods or Places
A short collection of links. This site also contains: Websites relevant to the History of Mathematics.

Mesopotamian Mathematics
“From the earliest tokens, through the development of Sumerian mathematics to the grand flowering in the Old Babylonian period, and on…”

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Math history > For elementary/middle-school students

Adding with the Abacus
“What did people do to save time working out more difficult problems before the calculator existed?”

Alexandria Jones and the History of Math
Several of my Alexandria Jones adventures involve math history. Browse down the page to see the stories I have posted, and watch for more coming soon.

Ancient Greek Mathematics
Selections from String, Straightedge & Shadow:

• Chapters 8, 9: Thales
• Chapters 11, 12: Pythagoras and his Theorem
• Chapter 13: Platonic Solids
• Chapter 14: The Irrationals
• Chapter 15: The Golden Mean
• Chapter 16: Archimedes
• Chapter 17: Eratosthenes

Archimedes & Large Numbers
A brief look at Archimedes, Avogadro, and Cantor. See Approximating Pi for an interactive demonstration, or Prehistoric Calculus: Discovering Pi for a more in-depth explanation.

Calendars
“Calendars were one of the earliest calculating devices developed by civilizations.”

Egyptian Math
Could you survive in the world of Egyptian numerals and mathematics? [Note to teachers: The Egyptian Math Worksheet Creator looks like fun!]

Eratosthenes’ sieve
Click on any number, and all its multiples (except the number itself) will disappear from the chart. See also: Murderous Maths Prime Numbers Page.

Eureka! The Achievements of Archimedes
Click “next” to read the pages one by one, or browse through the Index.

Famous Problems in the History of Mathematics
This site includes problems, paradoxes, and proofs that have inspired mathematicians through the ages, plus links for further exploration.

Fibonacci Activities
For explanations and more fun, see: Fibonacci Numbers and Nature.

Solid Gold Gnarly Math: The Gnarly Gnews
Free bi-monthly newsletter of math history with a twist of humor.

History of Fractions
“Did you know that fractions as we use them today didn’t exist in Europe until the 17th century?”

History of Measurement
To work effectively and share goods fairly, people had to find ways to measure their stuff. See also: Measure for Measure.

Leonardo da Vinci Activity
“Is the ratio of our arm span to our height really equal to 1?” See also: Teacher Lesson Plan and Leonardo’s Vitruvian Man.

Negative Numbers
“Among the earliest people to use negative numbers in calculations were the ancient Chinese.” See also: The History of Negative Numbers.

Pascal’s Triangle
Lessons and links for all grade levels. See also: All You Ever Wanted to Know About Pascal’s Triangle.

Pi, a Very Special Number
Over the centuries, mathematicians kept looking for better values for pi.

Platonic Solids
With printable nets, so you can make your own models. Part of the wonderful Maths is Fun site — take some time to explore!

Pythagoras
“Pythagoras believed that everything in the world could be explained by numbers.” See also: All Is Number.

ThinkQuest History of Mathematics
Brief overview of math history, with biographies of influential mathematicians and short online quizzes.

Women in Maths
“Ever wondered why stories about mathematicians always seem to be about men? …There were a few women who dared to go against the flow.”

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